\documentclass[english]{rug08pres}

\usepackage[utf8]{inputenc}
\usepackage{default}
\usepackage{graphicx}

\begin{document}

\facname{Faculty of Mathematics\\ and Natural Sciences}
\group{Multi-Agent Systems}
\titleslide {What's My Number?}
Ciar\'an Lier and Michiel van de Ree \\ \today

\slide[What's My Number: The Game]
\begin{itemize}
  \item So-called \textit{Headband deduction game}
  \item Nine numbered cards
  \item Three players, two cards each
  \item Twenty questions
    \begin{itemize}
      \item E.g. ``Do you see three consecutive numbers?''
    \end{itemize}
  \item Inspired by \textit{Code 777} \ldots
  \item \ldots which was in turn inspired by \textit{What's That on My Head}
    (1963)
\end{itemize}

\slide[]
\vspace{10mm}
\begin{tabular}{c l}
  \parbox{0.7\textwidth}{
    \vspace{10 mm}
    \textit{WToMH}-creator Richard Abbott:\\\\
    \textit{Playing this game is not simply learning a logic system and then using
      it to process the information you receive. It's a lot more difficult -- and a
      lot more creative. You must develop your own logic system and then use it
      to process the information you receive.
    }
  }
  &
  \raisebox{\dimexpr\ht\strutbox-\height\relax}{\includegraphics[width=0.3\textwidth]{img/wtomh6.jpg}}
  \\
  \hline
\end{tabular}

\slide[Sources of information]
\begin{itemize}
  \item Two sources of information:
    \begin{enumerate}
      \item Answers to questions
      \item The fact that nobody knows their cards
    \end{enumerate}
  \item Compare games in which only the first source is used to games in which
    both sources are used
  \item Use one Kripke model to model players' knowledge
  \item $S$ consists of all possible card distributions
    \begin{itemize}
      \item 7560 in total
    \end{itemize}
\end{itemize}

\slide[The epistemic step]
\begin{itemize}
  \item Muddy children-esque twist 
 \item Given that nobody knows their cards yet, remove all accessibility
   relations to and from states in which at least one player would have known
   her cards.
 \item At the end of turn, do this once or \ldots
 \item \ldots do it until the model does not change any more
\end{itemize}

\slide[Kooi's Choice]
\begin{itemize}
 \item Player chooses the question
 \item True state / Full model
\end{itemize}

\begin{tabular}{c c}
\includegraphics[width=11pc]{img/meaninfgainFull.jpg}
&
\includegraphics[width=11pc]{img/meaninfgainTrue.jpg}\\
\footnotesize Full model information gain &
\footnotesize True model information gain\\
\end{tabular}

\slide[Experiments]
\begin{itemize}
 \item Standard
  \subitem No magic
  \subitem Epistemagic once
  \subitem Infinite magic
 \item Kooi's Choice
  \subitem No magic (Full / True)
  \subitem Epistemagic once (Full / True)
  \subitem Infinite magic (Full / True)
\end{itemize}

\slide[Average number of turns]
\begin{center}
 \includegraphics[scale=0.38]{img/turns.jpg}
\end{center}

\slide[Who wins]
\begin{center}
 \includegraphics[scale=0.40]{img/winning-distribution.jpg}
\end{center}

\slide[Discussion]
\begin{itemize}
 \item Clear effect of epistemic logic
 \item Clear effect of Kooi's Choice
 \item Number of turns as measure
 \item Possible future work
  \subitem Implement a liar
  \subitem Implement set-like datastructure for state possibilities
\end{itemize}


\slide[]
\vspace{10mm}
\begin{tabular}{c l}
  \parbox{0.7\textwidth}{
    \centering
    \vspace{20mm}
    \huge
    Questions?
    \vspace{20mm}
  }
  &
  \raisebox{\dimexpr\ht\strutbox-\height\relax}{\includegraphics[width=0.3\textwidth]{img/wtomh6.jpg}}
  \\
  \hline
\end{tabular}
\slide[]
\vspace{10mm}
\begin{tabular}{c l}
  \parbox{0.7\textwidth}{
    \centering
    \vspace{20mm}
    \huge
    Questions?
    \vspace{20mm}
  }
  &
  \raisebox{\dimexpr\ht\strutbox-\height\relax}{\includegraphics[width=0.3\textwidth]{img/wtomh6.jpg}}
  \\
  \hline
\end{tabular}

\end{document}
